For designing a spectacle lens, it is performed to obtain by calculation a lens form which makes its optical performance as optimum as possible, within a range which satisfies a previously determined specification of the spectacle lens. As the specification of the spectacle lens, constraint conditions regarding the material, the prescription, or the like of the lens are given. In the case of a positive lens, a constraint condition on the center thickness of the lens is given as a further additional specification. Then, the designing of the spectacle lens is carried out while evaluating the optical performance of the lens using a predetermined function. Such a function is referred to as an evaluation function.
Specifically, a parameter which defines the spectacle lens is categorized in advance into a fixed parameter and a variable parameter. The fixed parameter is a constraint condition. Main items related to the optical lens design include a lens physicality/form factor (refractive power, Abbe number, specific gravity, lens surface form data, and the like), a prescription and fitting state related factor (lens diopter, astigmatic axis, addition, prism, base position, decentration, outside diameter, far vision PD, near vision PD, lens thickness, VR value (CR value+VC value)), an optical factor (diopter data of near vision, far vision, and the like) and other edging specific data. There may also be a case in which frame data (form, DBL, FPD, frame curve, and the like), a frame forward tilt angle, a bevel type and the like are added to design the lens. Then, first, a ray tracing method, a wave front tracing method or the like is used to set plural evaluation points having different lengths from an optical axis on a refractive surface of the spectacle lens. Next, while changing the value of the variable parameter by predetermined steps, a virtual spectacle lens, which is defined by a value of the variable parameter at this moment and a value of the fixed parameter, is assumed in each step.
Then, an evaluation value of the whole lens is obtained from values of the evaluation function at respective evaluation points of the virtual spectacle lens. Note that a function which defines an evaluation value of the whole lens using values of an evaluation function at respective evaluation points is referred to as a merit function. Then, the value of the variable parameter in a step in which the evaluation value becomes an optimum value is specified. In a preferable case, the merit function becomes an extremal value within a range which satisfies a specification. Accordingly, all the parameters which define the spectacle lens are obtained, and the lens is specified as a result.
A calculation which specifies the optimum value of the variable parameter as described above is referred to as an optimization calculation. At this time, it is preferred to use a method such as a damped least square method or the like. According to this method, the value of the variable parameter is efficiently specified by the least calculation amount. Such a calculation method is referred to as a least calculation. (For example, International Publication WO 00/62116, Japanese Examined Patent Publication No. Hei 02-38930, or the like.)
The inventor found the following problems in prior arts. Specifically, conventional evaluation functions (merit functions) are intended to evaluate optical performance of a spectacle lens by an aberration amount or the like of the lens itself. However, since the spectacle lens is essentially for visual acuity correction, the degree of deterioration of the visual acuity due to the aberration is more important than the aberration amount itself. It is thus preferable to implement not a simple evaluation function, but a kind of an evaluation function with respect to the visual acuity, namely, a function which prescribes a relation between the visual acuity while looking through an optical system and the aberration or the like of the optical system. Hereinafter, such a function is particularly referred to as a “visual acuity function.” Regarding the relation between the visual acuity and the aberration, a prior art 1 (Sloan, Louise, “Measurement of visual acuity: a critical review, A. M. A. Arch. Ophthal” (45(6): 704-725, 1951)) is known. In this document, an equation I is given as a visual acuity deteriorating part of a minimum separation threshold.2.8[sphere error+0.8(cyl error)]  equation I
In this equation I, it is defined that the sphere error=min (|T|, |S|), the cyl error=∥T|−|S∥, where T is a tangential error, and S is a sagittal error.
However, in this document, there are three problems as follows.
1. It does not refer to the chromatic aberration.
2. It does not refer to an eyeball motion (Listing's Law) of an astigmatic eye.
3. The “sphere error” and the “cyl error” are measured separately, but a visual acuity deterioration due to an interrelation between the “sphere error” and the “cyl error” is not measured.
Therefore, visual acuity deterioration data in which the “sphere error” and the “cyl error” are combined are unreliable, and a tentative theory of presumption is unconvincing.
Further, in Japanese Patent Laid-open No. Sho 58-24112, the following definition of a visual acuity V is disclosed.V=2−2·ΔR−ΔS  equation VI
Here, ΔR and ΔS are synonyms of the “sphere error” and the “cyl error” respectively in the equation I in the above-described prior art 1. Specifically, they are defined as ΔR=min (|S|, |T|), and ΔS=∥S|−|T∥.
In this publication, similarly to the above-described prior art 1, there is no reference to the chromatic aberration and the eyeball motion of an astigmatic eye. Further, it does not disclose any theory or reason (measured data or the like) as a basis to derive the equation of the visual acuity V, so that it is theoretically unreliable and unpractical.
Thus, it is a difficult problem to faithfully express the visual acuity using the aberration or the like. In other words, when it is tried to faithfully express the visual acuity, other biophenomena such as the eyeball motion and the like should be taken into consideration.
Further, among various kinds of aberrations, especially a relation between the chromatic aberration and the visual acuity is not ascertained yet.
For example, in Japanese Examined Patent Publication No. Sho 42-9416, a part of the above described equation I is defined as a Blur Index, and the “sphere error” and the “cyl error” to which the chromatic aberration is added are respectively defined as follows. Further, the relation of the Blue Index with fraction visual acuity V is shown by the following equation II to equation V.
                              Blur          ⁢                                          ⁢          Index                =                              sphere            ⁢                                                  ⁢            error                    +                      0.8            ⁢                                                  ⁢                          (                              cyl                ⁢                                                                  ⁢                error                            )                                                          equation        ⁢                                  ⁢        II                                          sphere          ⁢                                          ⁢          error                =                                                                            T                                            +                                              C                                            +                                              S                                                      2                    -                                                                                                      T                                                  +                                                    C                                                  -                                                    S                                                                                      2                                              equation        ⁢                                  ⁢        III                                          cyl          ⁢                                          ⁢          error                =                                                                    T                                      +                                        C                                      -                                        S                                                                                  equation        ⁢                                  ⁢        IV                                V        =                  20                      20            +                          56              ×              Blur              ⁢                                                          ⁢              Index                                                          equation        ⁢                                  ⁢        V            
Here, C is a chromatic aberration of magnification (transverse chromatic aberration), and is a value obtained by dividing a prism diopter of a deviation angle of a ray which penetrates a lens by an Abbe number. However, in this description, the tangential error is a function of pupil diameter, and although the chromatic aberration of magnification is mentioned to be irrelevant to this pupil diameter and the unit is actually different, the tangential error and the chromatic aberration of magnification are treated equally. In other words, one diopter of the tangential error and one prism diopter of the chromatic aberration of magnification are treated as equal amount of information, which are considered to respectively cause an equal amount of the deterioration of visual acuity.
This tentative theory has no reason based on any scientific data and cannot be verified, and the conclusion therein is also unconvincing. Further, it does not mention about consideration of the eyeball motion (Listing's Law) in calculation of an astigmatic diopter error.
Therefore, it is unusable for progressive lenses, atoric lenses or the like.
On the other hand, it is well known that the chromatic aberration is preferred to be small for visual acuity, and there is a few scientific study examples of an effect of the chromatic aberration on visual performance. Refer to “Kazuhiko Ukai, Hitoshi Ozu, Kaoru Nakajima, Osamu Shindo: Megane renzu no shikishuusa to shikinou ni oyobosu eikyou (the effects of spectacle lenses on chromatic aberration and visual performance) (KOHGAKU (Optics), 7(1): 21-28, 1977),” (hereinafter referred to as document 1).
However, the present situation is that, as described above, the relation of the both is not clearly understood to such a degree that at least it can be applied to designing of an actual optical system. In addition, it is considerable to ignore the chromatic aberration for simplification and define the visual acuity function with a focus only on aberrations other than the chromatic aberration. However, since it cannot be clearly said that there is no causal relation between the chromatic aberration and the visual acuity deterioration, it is hard to say that the visual acuity function ignoring the chromatic aberration is accurate.
Incidentally, the chromatic aberration has been ignored in optimization calculation in designing spectacle lenses. In other words, among conventional simple evaluation functions which are not the visual acuity function, there is no evaluation function which handles the chromatic aberration substantially as a variable parameter. It is conceivable, first, to be caused by that a selection range of an Abbe number which is closely correlated to the chromatic aberration is limited from the beginning to a certain degree in relation to the materials. Specifically, the degree of freedom of the Abbe number is smaller as compared to degrees of freedom of other factors. Therefore, in designing of optical systems, the Abbe number is not a variable parameter, but is fixed as a constraint condition (specification).
Also it is conceivable, second, to be caused by a recognition that imaging characteristics of a white light and a monochromatic light in an eyeball optical system are barely different. For more details about this, refer to the following document: “G. A. Fry: Progress in Optics, Vol VIII, p 112, ed. by E. Wolf, North-Holland Publishing Company, Amsterdam 1970” (hereinafter referred to as document 2), “KrausKopf J.: J. Opt. Soc. Amer., 52, 1046-1050 (1962) (hereinafter referred to as document 3), and “KrausKopf J.: J. Opt. Soc. Amer., 54, 715-716 (1964) (hereinafter referred to as document 4).”
This fact suggests at the same time that even if the Abbe number is sacrificed to a certain extent, a lens having a light weight and a good appearance which is made of a material having a high refractive power can increase the customer satisfaction more.
However, in the study of the inventor, it is proved that the evaluation or the design of optical systems based only on aberrations other than the chromatic aberration of magnification is entirely insufficient.
An object of the present invention is to provide a technique to properly perform evaluation of an optical system with respect to visual acuity in light of the chromatic aberration of magnification of the optical system. A further object of the present invention is to provide a technique to properly design an optical system in light of the chromatic aberration of magnification of the optical system.